BYTESM2  Philosophers Stone
One of the secret chambers in Hogwarts is full of philosopher’s stones. The floor of the chamber is covered by h × w square tiles, where there are h rows of tiles from front (first row) to back (last row) and w columns of tiles from left to right. Each tile has 1 to 100 stones on it. Harry has to grab as many philosopher’s stones as possible, subject to the following restrictions:
 He starts by choosing any tile in the first row, and collects the philosopher’s stones on that tile. Then, he moves to a tile in the next row, collects the philosopher’s stones on the tile, and so on until he reaches the last row.
 When he moves from one tile to a tile in the next row, he can only move to the tile just below it or diagonally to the left or right.
Input
The first line consists of a single integer T, the number of test cases. In each of the test cases, the first line has two integers. The first integer h (1 <= h <= 100) is the number of rows of tiles on the floor. The second integer w (1 <= w <= 100) is the number of columns of tiles on the floor. Next, there are h lines of inputs. The ith line of these, specifies the number of philosopher’s stones in each tile of the ith row from the front. Each line has w integers, where each integer m (0 <= m <= 100) is the number of philosopher’s stones on that tile. The integers are separated by a space character.
Output
The output should consist of T lines, (1 <= T <= 100), one for each test case. Each line consists of a single integer, which is the maximum possible number of philosopher’s stones Harry can grab, in one single trip from the first row to the last row for the corresponding test case.
Example
Input: 1 6 5 3 1 7 4 2 2 1 3 1 1 1 2 2 1 8 2 2 1 5 3 2 1 4 4 4 5 2 7 5 1 Output: 32 //7+1+8+5+4+7=32
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jayu_jd:
20170706 16:44:06
Good DP problem for beginners!! 

redligot2009:
20170704 02:37:01
Great problem for beginners to DP! 

shreyanshgeek:
20170703 13:17:30
AC in one go..!!


monukumar:
20170627 15:57:27
easy one!! attempt to build confidence in dp. :D 

xaer0_:
20170627 15:23:22
Had issues reading the input with C#. Converted code to C++ and it passed. Be careful reading the input if you're planning to solve this in C#. Last edit: 20170627 15:23:53 

anubhav112:
20170627 07:15:26
AC in one go.. :)


jaideeppyne:
20170622 19:23:05
Start from the last row of the matrix and go one row up at a time. Matrix with one column is an edge case :)


imshubhamk:
20170617 10:41:19
ac in one go....


kspoj:
20170616 16:57:43
Found an excellent explanation in Wikipedia 's examples for dp <3 :)


adarsh150:
20170610 10:28:11
What is problem in my code?????????

Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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